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- W4387596450 abstract "The pivot algorithm -- we also call it the pivot chain -- is an algorithm for approximately uniform sampling from $Omega _{N},$ the set of $N$-step self-avoiding walks on $mathbb{Z}^{d}$ ($N,$ $dgeq 1$). Based on this algorithm and the $G$ method, we construct another algorithm/chain, called the pivot$^{text{+}}$ algorithm/chain, for approximately uniform sampling from $Omega _{N},$ here, $Ngeq 2$. The pivot$^{text{+}}$ algorithm samples the pivot from the set $left{ 1,2,...,N-1right} $ according to the uniform probability distribution on this set while the pivot algorithm samples the pivot from the set $left{0,1,2,...,N-1right} $ according to the uniform probability distribution on this set, so, on the pivot, the pivot$^{text{+}}$ algorithm is better than the pivot algorithm. Further, we obtain another important thing, namely, the pivot$^{text{+}}$ algorithm/chain enters, at time $1$, a set $2d$ times smaller than $Omega _{N},$ and stays forever in this set, so, at times $1,2,...$ we work with a chain having a state space $2d$ times smaller than $Omega _{N}$. As to the speed of convergence, we conjecture that the pivot$^{text{+}}$ algorithm/chain is faster than the pivot algorithm/chain." @default.
- W4387596450 created "2023-10-13" @default.
- W4387596450 creator A5057931540 @default.
- W4387596450 date "2023-10-11" @default.
- W4387596450 modified "2023-10-14" @default.
- W4387596450 title "$G$ Method in Action: Pivot$^{text{+}}$ Algorithm for Self-avoiding Walk" @default.
- W4387596450 doi "https://doi.org/10.48550/arxiv.2310.07564" @default.
- W4387596450 hasPublicationYear "2023" @default.
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